Generalized processor sharing (GPS) has been considered as an ideal scheduling discipline based on its end-to-end delay bounds and fairness properties. Until recently, emulation of GPS in a packet server has been regarded as the ideal means of designing a packet-level scheduling algorithm to obtain low delay bounds and bounded unfairness. Strict emulation of GPS, as required in the weighted fair queueing (WFQ) scheduler, however, incurs a time-complexity of O(N) where N is the number of sessions sharing the link. Efforts in the past to simplify the implementation of WFQ, such as self-clocked fair queueing (SCFQ), have resulted in degrading its isolation properties, thus affecting the delay bound. In this paper we present a methodology for the design of scheduling algorithms that provide the same end-to-end delay bound as that of WFQ and bounded unfairness without the complexity of GPS emulation. The resulting class of algorithms, called rate-proportional servers (RPS's), are based on isolating scheduler properties that give rise to ideal delay and fairness behaviors. Network designers can use this methodology to construct efficient fair-queueing algorithms, balancing their fairness with implementation complexity. This work is completed in a sequel to this paper, where we present the detailed design and implementation of two novel scheduling algorithms based on the RPS framework.
Establishing a multicast tree in a point-to-point network of switch nodes, such as a wide-area ATM network, is often modeled as the NP-complete Steiner problem in networks.In this paper, we study algorithms for finding efficient multicast trees in the presence of constraints on the copying ability of the individual switch nodes in the network. We refer to this problem as the degree-constrained multicast tree problem and model it as the degree-constrained Steiner problem in networks. Steiner heuristics for the degree-constrained case are proposed and their simulation results for sparse, point-to-point networks are presented. The results are compared with respect to their quality of solution, cost (running time), and the number of test cases for which no solution could be found.The results of our research indicate that efficient multicast trees can be found in large, sparse networks with small multicast groups even with limited multicast capability in the individual switches. Some of the Steiner heuristics tested yielded degree-constrained multicast trees within 5% of the best heuristic solution found in most of the cases. Even when the fanout of each switch node was restricted to 2, the heuristics we used were able to generate efficient multicast trees in almost all our test networks. Surprisingly few test networks were unsolvable. In those cases where no solution was found by a heuristic, backtracking solved many of the remaining cases. Among the heuristics we used, degree-constrained versions of simple path-distance heuristics such as SPH and SPH-R provided the best tradeoffs between quality of solution and cost.
Loss of the routing protocol messages due to network congestion can cause peering session failures in routers, leading to route flaps and routing instabilities. We study the effects of traffic overload on routing protocols by quantifying the stability and robustness properties of two common Internet routing protocols, OSPF and BGP, when the routing control traffic is not isolated from data traffic. We develop analytical models to quantify the effect of congestion on the robustness of OSPF and BGP as a function of the traffic overload factor, queueing delays, and packet sizes. We perform extensive measurements in an experimental network of routers to validate the analytical results. Subsequently we use the analytical framework to investigate the effect of factors that are difficult to incorporate into an experimental setup, such as a wide range of link propagation delays and packet dropping policies. Our results show that increased queueing and propagation delays adversely affect BGP's resilience to congestion, in spite of its use of a reliable transport protocol. Our findings demonstrate the importance of selective treatment of routing protocol messages from other traffic, by using scheduling and utilizing buffer management policies in the routers, to achieve stable and robust network operation.
In this paper, we propose and evaluate ARIES, a heuristic for updating multicast trees dynamically in large pointto-point networks. The algorithm is based on monitoring the accumulated damage to the multicast tree within local regions of the tree as nodes are added and deleted, and triggering a rearrangement when the number of changes within a connected subtree crosses a set threshold. We derive an analytical upper-bound on the competitiveness of the algorithm. We also present simulation results to compare the averagecase performance of the algorithm with two other known algorithms for the dynamic multicast problem, GREEDY and EBA (Edge-Bounded Algorithm). Our results show that ARIES provides the best balance among competitiveness, computational e ort, and changes in the multicast tree after each update.
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